The classification of waves of frequencies 2 Hz , 2 kHz , 2 MHz , 2 GHz , 2 THz , 2 PHz , 2 EHz , 2 ZHz and 2 YHz on the electromagnetic spectrum and the classification of waves of wavelengths 2 km , 2 m , 2 mm , 2 μm , 2 nm , 2 pm , 2 fm , and 2 am

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Answer 1

Question

Chapter 24, Problem 38P

To determine

The classification of waves of frequencies 2 Hz , 2 kHz , 2 MHz , 2 GHz , 2 THz , 2 PHz , 2 EHz , 2 ZHz and 2 YHz on the electromagnetic spectrum and the classification of waves of wavelengths 2 km , 2 m , 2 mm , 2 μm , 2 nm , 2 pm , 2 fm , and 2 am

Expert Solution & Answer

Answer to Problem 38P

The classification of waves on the basis of frequency is shown below.

Frequency, f	Wavelength, λ=cf		Classification
2 Hz	150 Mm		Radio
2 kHz = 2×103 Hz		150 km		Radio
2 MHz = 2×106 Hz		150 m		Radio
2 GHz = 2×109 Hz		150 cm		Microwave
2 THz = 2×1012 Hz		150 μm		Infrared
2 PHz = 2×1015 Hz		150 nm		Ultraviolet
2 EHz = 2×1018 Hz		150 pm		X-ray
2 ZHz = 2×1021 Hz		150 fm		Gamma ray
2 YHz = 2×1024 Hz		150 am		Gamma ray

The classification of waves on the basis of wavelength is shown below.

Wavelength, λ	Frequency, f=cλ		Classification
2 km = 2×103 m	1.5×105 Hz		Radio
2 m = 2×100 m		1.5×108 Hz		Radio
2 mm = 2×10−3 m		1.5×1011 Hz		Microwave
2 μm = 2×10−6 m		1.5×1014 Hz		Infrared
2 nm = 2×10−9 m		1.5×1017 Hz		Ultraviolet/ X-ray
2 pm = 2×10−12 m		1.5×1020 Hz		X-ray/Gamma ray
2 fm = 2×10−15 m		1.5×1023 Hz		Gamma ray
2 am = 2×10−18 m		1.5×1026 Hz		Gamma ray

Explanation of Solution

The formula to calculate the wavelength is,

λ=cf (1)

Here,

c is the speed of light.

f is the frequency of the wave.

Substitute 3×108 m/s for c and 2 Hz for f in equation (1) to find the value of λ .

λ=(3×108 m/s)(2 Hz)=15×107 m×10−6 Mm1 m=150 Mm

Substitute 3×108 m/s for c and 2 kHz for f in equation (1) to find the value of λ .

λ=(3×108 m/s)(2 kHz×103 Hz1 kHz)=15×104 m×10−3 km1 m=150 km

Substitute 3×108 m/s for c and 2 MHz for f in equation (1) to find the value of λ .

λ=(3×108 m/s)(2 MHz×106 Hz1 MHz)=1.5×102 m=150 m

Substitute 3×108 m/s for c and 2 GHz for f in equation (1) to find the value of λ .

λ=(3×108 m/s)(2 GHz×109 Hz1 GHz)=1.5×10−1 m×103 cm1 m=150 cm

Substitute 3×108 m/s for c and 2 THz for f in equation (1) to find the value of λ .

λ=(3×108 m/s)(2 THz×1012 Hz1 THz)=1.5×10−4 m×106 μm1 m=150 μm

Substitute 3×108 m/s for c and 2 PHz for f in equation (1) to find the value of λ .

λ=(3×108 m/s)(2 PHz×1015 Hz1 PHz)=1.5×10−7 m×109 nm1 m=150 nm

Substitute 3×108 m/s for c and 2 EHz for f in equation (1) to find the value of λ .

λ=(3×108 m/s)(2 EHz×1018 Hz1 EHz)=1.5×10−10 m×1012 pm1 m=150 pm

Substitute 3×108 m/s for c and 2 ZHz for f in equation (1) to find the value of λ .

λ=(3×108 m/s)(2 ZHz×1021 Hz1 ZHz)=1.5×10−13 m×1015 fm1 m=150 fm

Substitute 3×108 m/s for c and 2 YHz for f in equation (1) to find the value of λ .

λ=(3×108 m/s)(2 YHz×1024 Hz1 YHz)=1.5×10−16 m×1018 am1 m=150 am

From the above calculation, the table for the wavelength can be deduces and the respective classification of waves is shown.

Frequency, f	Wavelength, λ=cf		Classification
2 Hz	150 Mm		Radio
2 kHz = 2×103 Hz		150 km		Radio
2 MHz = 2×106 Hz		150 m		Radio
2 GHz = 2×109 Hz		150 cm		Microwave
2 THz = 2×1012 Hz		150 μm		Infrared
2 PHz = 2×1015 Hz		150 nm		Ultraviolet
2 EHz = 2×1018 Hz		150 pm		X-ray
2 ZHz = 2×1021 Hz		150 fm		Gamma ray
2 YHz = 2×1024 Hz		150 am		Gamma ray

The formula to calculate the frequency is,

f=cλ (2)

Here,

c is the speed of light.

λ is the wavelength of the wave.

Substitute 3×108 m/s for c and 2 km for λ in equation (2) to find the value of f .

λ=(3×108 m/s)(2 km×103 m1 km)=1.5×105 Hz

Substitute 3×108 m/s for c and 2 m for λ in equation (2) to find the value of f .

λ=(3×108 m/s)(2 m)=1.5×108 Hz

Substitute 3×108 m/s for c and 2 mm for λ in equation (2) to find the value of f .

λ=(3×108 m/s)(2 mm×10−3 m1 mm)=1.5×1011 Hz

Substitute 3×108 m/s for c and 2 μm for λ in equation (2) to find the value of f .

λ=(3×108 m/s)(2 μm×10−6 m1 μm)=1.5×1014 Hz

Substitute 3×108 m/s for c and 2 nm for λ in equation (2) to find the value of f .

λ=(3×108 m/s)(2 nm×10−9 m1 nm)=1.5×1017 Hz

Substitute 3×108 m/s for c and 2 pm for λ in equation (2) to find the value of f .

λ=(3×108 m/s)(2 pm×10−12 m1 nm)=1.5×1020 Hz

Substitute 3×108 m/s for c and 2 fm for λ in equation (2) to find the value of f .

λ=(3×108 m/s)(2 am×10−15 m1 am)=1.5×1023 Hz

Substitute 3×108 m/s for c and 2 am for λ in equation (2) to find the value of f .

λ=(3×108 m/s)(2 am×10−18 m1 am)=1.5×1026 Hz

From the above calculation the table for the frequency can be deduces and the respective classification of waves is shown below.

Wavelength, λ	Frequency, f=cλ		Classification
2 km = 2×103 m	1.5×105 Hz		Radio
2 m = 2×100 m		1.5×108 Hz		Radio
2 mm = 2×10−3 m		1.5×1011 Hz		Microwave
2 μm = 2×10−6 m		1.5×1014 Hz		Infrared
2 nm = 2×10−9 m		1.5×1017 Hz		Ultraviolet/ X-ray
2 pm = 2×10−12 m		1.5×1020 Hz		X-ray/Gamma ray
2 fm = 2×10−15 m		1.5×1023 Hz		Gamma ray
2 am = 2×10−18 m		1.5×1026 Hz		Gamma ray

Conclusion:

Therefore, the table of classification of waves with the frequencies is shown below.

Frequency, f	Wavelength, λ=cf		Classification
2 Hz	150 Mm		Radio
2 kHz = 2×103 Hz		150 km		Radio
2 MHz = 2×106 Hz		150 m		Radio
2 GHz = 2×109 Hz		150 cm		Microwave
2 THz = 2×1012 Hz		150 μm		Infrared
2 PHz = 2×1015 Hz		150 nm		Ultraviolet
2 EHz = 2×1018 Hz		150 pm		X-ray
2 ZHz = 2×1021 Hz		150 fm		Gamma ray
2 YHz = 2×1024 Hz		150 am		Gamma ray

Therefore, the table of classification of waves with the wavelengths is shown below.

Wavelength, λ	Frequency, f=cλ		Classification
2 km = 2×103 m	1.5×105 Hz		Radio
2 m = 2×100 m		1.5×108 Hz		Radio
2 mm = 2×10−3 m		1.5×1011 Hz		Microwave
2 μm = 2×10−6 m		1.5×1014 Hz		Infrared
2 nm = 2×10−9 m		1.5×1017 Hz		Ultraviolet/ X-ray
2 pm = 2×10−12 m		1.5×1020 Hz		X-ray/Gamma ray
2 fm = 2×10−15 m		1.5×1023 Hz		Gamma ray
2 am = 2×10−18 m		1.5×1026 Hz		Gamma ray

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Answer 2

Question

Chapter 24, Problem 38P

To determine

The classification of waves of frequencies 2 Hz , 2 kHz , 2 MHz , 2 GHz , 2 THz , 2 PHz , 2 EHz , 2 ZHz and 2 YHz on the electromagnetic spectrum and the classification of waves of wavelengths 2 km , 2 m , 2 mm , 2 μm , 2 nm , 2 pm , 2 fm , and 2 am

Expert Solution & Answer

Answer to Problem 38P

The classification of waves on the basis of frequency is shown below.

Frequency, f	Wavelength, λ=cf		Classification
2 Hz	150 Mm		Radio
2 kHz = 2×103 Hz		150 km		Radio
2 MHz = 2×106 Hz		150 m		Radio
2 GHz = 2×109 Hz		150 cm		Microwave
2 THz = 2×1012 Hz		150 μm		Infrared
2 PHz = 2×1015 Hz		150 nm		Ultraviolet
2 EHz = 2×1018 Hz		150 pm		X-ray
2 ZHz = 2×1021 Hz		150 fm		Gamma ray
2 YHz = 2×1024 Hz		150 am		Gamma ray

The classification of waves on the basis of wavelength is shown below.

Wavelength, λ	Frequency, f=cλ		Classification
2 km = 2×103 m	1.5×105 Hz		Radio
2 m = 2×100 m		1.5×108 Hz		Radio
2 mm = 2×10−3 m		1.5×1011 Hz		Microwave
2 μm = 2×10−6 m		1.5×1014 Hz		Infrared
2 nm = 2×10−9 m		1.5×1017 Hz		Ultraviolet/ X-ray
2 pm = 2×10−12 m		1.5×1020 Hz		X-ray/Gamma ray
2 fm = 2×10−15 m		1.5×1023 Hz		Gamma ray
2 am = 2×10−18 m		1.5×1026 Hz		Gamma ray